Three computational approaches to weakly nonlocal Poisson brackets

Abstract

We compare three different ways of checking the Jacobi identity for weakly nonlocal Poisson brackets using the theory of distributions, of pseudodifferential operators and of Poisson vertex algebras, respectively. We show that the three approaches lead to similar computations and same results.

arXiv comment47 pages

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Cited by in corpus (8)

• Applications of Nijenhuis geometry III: Frobenius pencils and compatible non-homogeneous Poisson structures
• Weakly nonlocal Poisson brackets: tools, examples, computations
• WDVV equations and invariant bi-Hamiltonian formalism
• Miura-reciprocal transformations and localizable Poisson pencils
• Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics
• Some Remarks on the Operators' Formalism for Nonlocal Poisson Brackets
• WDVV equations: Hamiltonian operators and symbolic computations
• Bi-Hamiltonian structures of WDVV-type